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Proof step 7 from proof middle-coef-max_exp-equality (previous step)

j ≤ 2 * j ∧ 0 ≤ j → fac(2 * j - j) * fac(j) | fac(2 * j), i ^ i0 ≤ 2 * j, 2 * j < i ^ (i0 + 1), prime(i), i ^ i0 < i ^ (i0 + 1), 0 ≤ i0, 0 < j, 0 ≤ j ⊦ max_exp(i, fac(2 * j) / (fac(2 * j - j) * fac(j))) = Σ countFun(1, i0, λ i0. (2 * j) / i ^ i0 - 2 * j / i ^ i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%le-same-01: ⊦ 0 < i → (i ≤ i * j ↔ 1 ≤ j); from specification int-mult